My Math Forum Solve this recurrence relation with repeated subsitution

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 September 15th, 2016, 05:24 PM #1 Newbie   Joined: Sep 2016 From: CO Posts: 6 Thanks: 0 Solve this recurrence relation with repeated subsitution $\displaystyle \sqrt(n)T(\sqrt(n)+n$ I've tried what I think is right, but I came up with: $\displaystyle (n^{1/2}*n^{1/2^{2}}*...*n^{1/2^{k}})T(n^{1/2^{k}})+(n^{1/2^{k-1}}+...+n^{1/2}+n)$ And I have no idea how to find the pattern of that so I'm hoping I'm wrong.
 September 15th, 2016, 05:49 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond What recurrence relation?! You've given an expression in $n$. Why did you post this in Linear Algebra?
 September 15th, 2016, 06:27 PM #3 Newbie   Joined: Sep 2016 From: CO Posts: 6 Thanks: 0 This is for my Analysis of Algorithms class. I'm not sure where else to put it so I was hoping Linear was related.
 September 15th, 2016, 06:28 PM #4 Newbie   Joined: Sep 2016 From: CO Posts: 6 Thanks: 0 As for the format, does this change anything? $\displaystyle T(n) = \sqrt(n)T\sqrt(n)+n$ for $\displaystyle n\leq 2$
 September 15th, 2016, 06:38 PM #5 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond Um...shouldn't the $n$ have a subscript?
 September 15th, 2016, 06:49 PM #6 Newbie   Joined: Sep 2016 From: CO Posts: 6 Thanks: 0 no It is solved in the first method presented here. I understand this simple example, but idk about the one I posted.
 September 15th, 2016, 06:58 PM #7 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond The system caught your link. I've approved the post. Just to be sure we're on the same page, do you intend $$T(n)=\sqrt nT(\sqrt n)+n$$ ?
 September 15th, 2016, 07:04 PM #8 Newbie   Joined: Sep 2016 From: CO Posts: 6 Thanks: 0 Yes, sorry I'm not good at Latex yet.
 September 16th, 2016, 02:03 PM #9 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond From W|A: $$T(n)=\frac{n}{e^2}+\frac{n\log(\log(n))}{\log(2) }$$ I've verified it with a CAS and I don't know how to compute it. It seems like a somewhat (at least) difficult problem.
 September 16th, 2016, 02:35 PM #10 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,638 Thanks: 2623 Math Focus: Mainly analysis and algebra The OP's relation is invalid for n=1. It also fails to define T for most values of n as far as I can see.

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